I never played 4e. I never bought 4e. I never even really properly read a 4e book (although I did flip through some of them and read bits and pieces of some of them. And talked a fair bit with gamers who did.)
In general, I say that the legacy of 4e was the Great D&D Schism, wherein D&D players, who were already bleeding severely away from 3.5 as it was near the end of that particular era, were split into various groups that seem to be pretty much irreconcilable. Enough moved to 4e to make that a significant faction of the former D&D player base. Enough moved to the OSR (although frankly, they were probably already doing that prior to the release, or even the announcement of 4e.) Enough moved to Pathfinder when that option became available. And, frankly--a fair number stayed with d20 even though it was no longer current or supported. It is, after all, fairly compatible with Pathfinder material still, and there is tons of stuff in print available to use that you shouldn't need to always need something newly released to have more than enough information to keep gaming indefinitely.
Personally, 4e exacerbated a lot of the problems I already had with 3e. 30 levels instead of 20? I'm already only interested in about 10 of them as it is. Tactical gameplay that turns into something that feels like Warhammer Fantasy Quest, or some other token and board game instead of an RPG? Big lists of character powers? Literally printed on cards? No possibility of "theater of the mind" combat? Blegh.
But I'm not making this post to rag on 4e; rather, there are at least two innovations that 4e brings to the table that (hopefully) will be around improving D&D games from here to the end of time.
First; the concept of the minion. I had independently stumbled across the concept of "Schrödinger's stats"--a necessary innovation for my winging it style of GMing. In this paradigm, you don't need pregenerated stat-blocks; you can simply make up stats on the fly for many opponents. I had also independently stumbled across a future development of that; the notion that you don't even need to track hitpoints; whether you just made them up on the fly or not. Rather, you can have opponents go down when you start to feel like the combat is wearing on the players and it's not fun anymore (actually; hopefully right before that happens, if you're perceptive enough.) I hadn't yet, however, come up with the notion that they don't even need hitpoints at all, and the idea of minions that automatically drop if they're hit hadn't quite occurred to me yet.
Granted, if you do use "theater of the mind" style combat, as I prefer, then it's a little harder to utilize big hordes of minions (although not impossible) but smaller swarms of minions is still a very useful tool. This is one aspect of 4e that I hope to see more of as editions continue on.
The second notion is the healing surge. In d20, I'd utilized action points as healing surges, or rather, one of the potential uses of action points mimicked healing surges by functioning as an instant potion of cure light wounds, essentially. Since my setting doesn't have clerics or potions, this was even more useful to me than it was to a standard D&D player--although it was a useful use of action points in any game. When I input Heroism Points into my m20 game, I did something different. However, I wasn't really super happy with the results. On further thought, I've updated my m20 file (again--now at version 1.1.6) to have Heroism Points work pretty much exactly the way Action Points used to work in my old d20 houserules document. Bingo!
Now, an early contender for an innovation of 5e that I hope is implemented as well as promised, and which I hope (if so) becomes part of the core DNA for D&D going forward is "bounded accuracy." Of course, other games besides D&D already had this in spades, but it's a new feature to the specific lexicon of D&D. But that's a discussion for another post sometime. And my m20 doesn't do anything to address bounded accuracy other than arbitrarily cap leveling at 10th instead of allowing it to go farther.